Stochastically pumped adaptation and directional motion of molecular machines

Abstract

Recent developments in synthetic molecular motors and pumps have sprung from a remarkable confluence of experiment and theory. Synthetic accomplishments have facilitated the ability to design and create molecules, many of them featuring mechanically bonded components, to carry out specific functions in their environment-walking along a polymeric track, unidirectional circling of one ring about another, synthesizing stereoisomers according to an external protocol, or pumping rings onto a long rod-like molecule to form and maintain high-energy, complex, nonequilibrium structures from simpler antecedents. Progress in the theory of nanoscale stochastic thermodynamics, specifically the generalization and extension of the principle of microscopic reversibility to the single-molecule regime, has enhanced the understanding of the design requirements for achieving strong unidirectional motion and high efficiency of these synthetic molecular machines for harnessing energy from external fluctuations to carry out mechanical and/or chemical functions in their environment. A key insight is that the interaction between the fluctuations and the transition state energies plays a central role in determining the steady-state concentrations. Kinetic asymmetry, a requirement for stochastic adaptation, occurs when there is an imbalance in the effect of the fluctuations on the forward and reverse rate constants. Because of strong viscosity, the motions of the machine can be viewed as mechanical equilibrium processes where mechanical resonances are simply impossible but where the probability distributions for the state occupancies and trajectories are very different from those that would be expected at thermodynamic equilibrium. molecular machine | stochastic pumping | kinetic asymmetry The molecular machines necessary for life must carry out their function in the fluctuating environment of a biological cell. Nowhere is the dynamic aspect of biology at the molecular level more evident than in the bilayer membrane surrounding most cells and organelles, a small portion of which is shown schematically in Fig. 1. Three transmembrane proteins are included in the depiction: (i) an ion channel that provides a conduit for conduction of ions across the membrane; (ii) a molecule that facilitates the transport of some substance, S, across the membrane; and (iii), an NaATPase that uses energy from ATP hydrolysis to maintain ion gradients across the membrane. The transporter acts as a catalyst to reduce the barrier for transport of S. In and of itself, the transporter cannot drive the substance S from low to high chemical potential. The transporter, however, is near a possible source of energy, the ion channel. The ion channel provides a path for conduction of ions from high to low electrochemical potential, thus dissipating energy. Every time the ion channel opens or closes, the local electric field across the membrane changes, and because the flow of ions down the electrochemical gradient when the channel is open dissipates energy, the resulting ...

The Physics and Physical Chemistry of Molecular Machines

“…These and similar ideas on the effects of external perturbations [87,88] have led to recent advances in the design and synthesis of molecular machines, including those that use dissipation of energy to achieve self-assembly. [89,90] One system, in particular, on which we shall focus, has been termed a synthetic molecular pump, where externally driven oscillations of the redox potential leads to formation and maintenance of a strongly disfavored non-equilibrium structure.…”

The Art of Building Small: From Molecular Switches to Motors (Nobel Lecture)

“…and face the question "How to control motion"? In the molecular world where Brownian motion rules and noting that biological motors commonly operate as Brownian ratchets, [10] the design of molecular systems with precisely defined translational and rotary motion is the main challenge. [11] Making the leap from molecules to dynamic molecular systems while drawing lessons from life itself,a ni mportant challenge ultimately is to achieve out-of-equilibrium phenomena.…”

Escapement mechanisms: Efficient free energy transduction by reciprocally‐coupled gating

“…Such “overdamped systems” therefore remain in mechanical equilibrium throughout their range of motion and on time scales longer than a few microseconds. Consequently, the near‐equilibrium terms of the Onsager‐Machlup theory furnish an unexpectedly appropriate description even if the source driving their motion is far from equilibrium with the path in which the system moves, and their fluxes are proportional to the forces that cause them …”